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2015 Ding projective modules with respect to a semidualizing bimodule
Chunxia Zhang, Limin Wang, Zhongkui Liu
Rocky Mountain J. Math. 45(4): 1389-1411 (2015). DOI: 10.1216/RMJ-2015-45-4-1389

Abstract

Let $R$ and $S$ be rings and ${}_SC_R$ a faithfully semidualizing bimodule. A left $S$-module $M$ is called \textit{Ding $C$-projective} if there exists an exact sequence of $C$-projective left $S$-modules \[ X=\cdots \rightarrow C\otimes_{R} P_{1}\rightarrow C\otimes_{R} P_{0}\rightarrow C\otimes_{R} P^{0}\rightarrow C\otimes_{R} P^{1}\rightarrow \cdots \] such that $M\cong\mbox{Coker\,}(C\otimes_{R} P_{1}\rightarrow C\otimes_{R} P_{0})$ and the complexes $\mbox{Hom}_S(C\otimes_{R}P, X)$ and $\mbox{Hom}_S(X,C\otimes_{R}F)$ are exact for any projective left $R$-module $P$ and any flat left $R$-module $F$. The properties of Ding $C$-projective modules and dimensions are given. Among others, the Foxby equivalences between some subclasses of the Auslander class and the Bass class are also investigated.

Citation

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Chunxia Zhang. Limin Wang. Zhongkui Liu. "Ding projective modules with respect to a semidualizing bimodule." Rocky Mountain J. Math. 45 (4) 1389 - 1411, 2015. https://doi.org/10.1216/RMJ-2015-45-4-1389

Information

Published: 2015
First available in Project Euclid: 2 November 2015

zbMATH: 1343.16008
MathSciNet: MR3418200
Digital Object Identifier: 10.1216/RMJ-2015-45-4-1389

Subjects:
Primary: 16D40, 16E10

Rights: Copyright © 2015 Rocky Mountain Mathematics Consortium

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Vol.45 • No. 4 • 2015
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